Symmetric Definition and 539 Threads

Homework Statement Help! I was wondering if anyone can help me integrate: ∫ x^2tan x + y^3 +4 dA, where D is the region represented by D = {(x,y)|x2+y2≤2} Homework Equations I think that the area is symmetric, and so basically you only need to evalute from 0≤ x ≤ √(2-y^2) and 0≤ y ≤...

Homework Statement A figure is attached. The symmetric system consists of 4 massless rodes with length 'L',the purple thing is a spring(the spring constant is k),when the system is at rest theta=45 deg. the system starts to rotate with angular speed 'w',the rodes are pushing on the...

Homework Statement A particle of mass m moves in three dimensions in a potential energy field V(r) = -V0 r< R 0 if r> R where r is the distance from the origin. Its eigenfunctions psi(r) are governed by \frac{\hbar^2}{2m} \nabla^2 \psi + V(r) \psi = E \psi ALL in spherical coords...

In 4 dimensions, a spacetime can have a maximum of 10 linearly independent Killing vectors. Are there known examples of spacetimes (satisfying Einstein's equation) with 7, 8, or 9 Killing vectors? I know FRW cosmologies have 6 Killing vectors, but I'm looking for something a bit more symmetric...

1) Use the fact that the form factor, F(q), is the Fourier transform of the normalised charge distribution p(r), which in the spherically symmetric case gives , F(q) = \int \frac{4\pi\hbar r}{q}p(r)sin(\frac{qr}{\hbar}) dr to find an expression for F(q) for a simple model of the proton...

Show agrebraically that symmetric difference quotient produces the exact derivative f'(x) = 2ax+b for the quadractic function f(x) = ax^2+bx+c i know that: f(a + h) - f(a - h) Symmetric Difference Quotient = -------------------...

Let p1,p2 be two density matrices and M be a real, symmetric matrix. Now, <<p1|[M,p2]>>= <<p1|M*p2>>-<<p1|p2*M>>= Tr{p1*M*p2}-Tr{p1*p2*M}= 2i*Tr{(Im(p1|M*p2))}. Why is it that this works out as simply as (x+iy)-(x-iy)? How is Tr{p1*p2*m}=conjugate(Tr{p1*M*p2})? I can't seem to figure...

I would like to know the statement is always true or sometimes false, and what is the reason: A is a square matrix P/S: I denote transpose A as A^T 1)If AA^T is singular, then so is A; 2)If A^2 is symmetric, then so is A.

Hi, I am having trouble with the question above. In general, I have trouble with questions like: What is the basis for all nxn matrices with trace 0? What is the dimension? What is the basis of all upper triangular nxn matrices? What is the dimension? Please help!

Lets say you have a function that is constant except at interval [-2,2] where it drains down to infinity. The whole function is reflected symetrically at x=0. Is the limit of this function, as x approaches 0, negative infinity?

A few friends have expressed an interest in exploring the geometry of symmetric spaces and Lie groups as they appear in several approaches to describing our universe. Rather than do this over email, I've decided to bring the discussion to PF, where we may draw from the combined wisdom of its...

Forgive me if I have used the wrong phrase to characterize the phenomenon. If my understanding is flawed, someone please correct me. From what I understand, theory postulates that all points in space will measure a red shift. How has this been tested? It seems to me such an effect would be...

Show that every eigenvalue of A is zero iff A is nilpotent (A^k = 0 for k>=1) i m having trouble with going from right to left (left to right i got) we know that det A = product of the eignevalues = 0 when we solve for the eigenvalues and put hte characteristic polynomial = 0 then det...

Ok so here's one of the questions we've been assigned... So I can graphically see what this relation looks like, and from that I've shown it's reflexive. Now I'm working on proving it as being symmetric, but I can't put it into words. b) ~ is symmetric. Well we want to show that aRb ->...

I have this problem that i need to prove and i don't even know where to start. So I have to show that the symmetric algebra ( Sym V ) is isomorphic to free commutative R-algebra on the set {x1, ..., xn}. Now i know that Sym V could be regarded as +Sym^n V for n>=0. And then we need to...

Is the the following definition correct? Two elements a and b of a group G are said to be CONJUGATE if there exists g in G such that a=gbg^{-1}. For instance, show that all elements in the symmetric group S5 of order 6 conjugate.

Let A be an nxn skew symmetric mx.(A^T=-A). i) Show that if X is a vector in R^n then (X,AX)=0 ii) Show that 0 is the only possible eigenvalue of A iii)Show that A^2 is symmetric iv)Show that every eigenvalue of A^2 is nonpositive. v)Show that if X is an eigenvector of A^2 , then so is AX...

I haven't read this yet, but I'm putting it up here for discussion as it seems so fascinating: PT-Symmetric Versus Hermitian Formulations of Quantum Mechanics Carl M. Bender, Jun-Hua Chen, Kimball A. Milton A non-Hermitian Hamiltonian that has an unbroken PT symmetry can be converted by...

I've got to proof the following: Let f be a monic polynomial in Q[X] with deg(f) = n different complex zeroes. Show that the sign of the discriminant of f is equal to (-1)^s, with 2s the number of non real zeroes of f. I know the statement makes sense, because the discriminant is a...

(1) If A is an n x n matrix, then prove that (A^T)A (i.e., A transpose multiplied by A) is symmetric. (2) Let S be the set of symmetric n x n matrices. Prove that S is a subspace of M, the set of all n x n matrices. (3) What is the dimension of S? (4) Let the function f : M-->S be defined by...

for a symmetrical potential with one electron, i know that the wavefunctions are symmetric or antisymmetric. for the ground state why is the wavefunction symmetric? Also, if you add a second electron that is non-interacting, (why) does it have the same wavefunction as the first electron?

done Hi there, I am have trouble with a proof. I have some steps done, but I am not sure if I am aproaching this correctly. the question is: Show that the matrix of any reflection in R^n is a symmetric matrix. I know that F(x) = Ax + b is an isometry where A is an Orthoganol matrix...

How can I prove that that every symmetric real matrix is diagonalizable? Thanks in advance

Let M2 be the vector space of 2 x 2 matrices.How to find a basis for the subspace of M2 consisting of symmetric matrices. The problem it creates for me is that i ca guess the solution but i don't have any symstematic procedure in mind... :cry: Pls help

show that B_{ij} can be written as the sum of a symmetric tensor B^S_{ij} and an antisymmetric tensor B^A_{ij} i don't know how to do this one. for a symmetric tensor we have B^S_{ij} = B^S_{ji} and for an antisymmetric tensor we have B^A_{ij} = -B^A_{ji} the only thing my book...

Hello all. I'm stuck with this excercise that is asking me to proof that the determinant of the nxn matrix with a's on the diagonal and everywhere else 1's equals to: |A| = (a + n - 1).(a-1)^(n-1) So the matrix should look something like: [a 1 1.. 1] [1 a 1.. 1] [: ... :] [1 ..1 1...

I am not sure if my title to this thread is appropriate for the question I am about to ask, but it is what we are currently studying in my Quantum Mechanics class so here it goes. Two non-interacting particles with mass m, are in 1-d potential which is zero along a length 2a and infinite...

Question: Let R be a symmetric relation on set A. Show that R^n is symetric for all positive integers n. My "solution": Suppose R is symmetric, \exists a,b \in A ((a,b) \in R \wedge (b,a) \in R) For n=1, R^1=R. Next, assume that (a,b) and (b,a) \in R^k, for k a possitive...

Explain why the permutations (1 2) and (1 2 ... n) generate all of Sn, the symmetric group (the group of all permutations of the numbers {1,2,...,n}? Perhaps something to do with the fact that (1 2 ... n) = (1 2) (1 3) ... (1 n)? Other than that I haven't got a clue - help! (please!) Thanks

If you have a symmetric, nonsingular matrix A, is it always possible to find a matrix B such that B^T A B = 1, where 1 is the identity?

Guys, I'm trying (just for fun) to map out quantitatively from each traveller's perspective what happens in the following situation. Imagine the classic twins paradox, with triplets instead of twins, but not for the purposes of avoiding the turn-around. In my question, Triplet A stays on Earth...

Does anyone know of a reference (or website) where I can find the Ricci tensor/scalar for a static, circularly symmetric spacetime (2 + 1) ? Thanks:)

Dear forum contributer, The binding energy of a heavy nucleus is about 7 Mev per nucleon, whereas the binding energy of a medium-weight nucleus is about 8 Mev per nucleon. Therefore, the total kinetic energy liberated when a heavy nucleus undergoes symmetric fission is most nearly (A) 1876...

1.) SYMMETRY (think a arm or leg extention) + REACTION (think a cupboard) = proportion 2.) Question: Water (action) + a Cup's Rim (reaction) = what Proportion ? Answer: A plural format. 3.) Symmetry is a case of action and reaction = proportion. 4.) Merriam-Webster Online...

I have a question concerning the stationary states of a spherically symmetric potential (V=V(r), no angular dependence) By separation of variables the eigenfunctions of the angular part of the Shrödinger equation are the spherical harmonics. However, (apart from Y^0_0) these are not...

these are some review questions for an exam: 1.why are s-orbital spherically symmetric? 2.What is the probability of finding an electron at or very near to the nucleus? (1s, 2s, 2p... 3.Why does the curve for 1s go to zero for r-> 0? (the curve of the probability density associated...

Let me see if I can make it clearer. Problem 5.5 In David Griffiths “Introduction to Quantum Mechanics” says: Imagine two non interacting particles, each of mass m, in the infinite square well. If one is in the state psin and the other in state psim orthogonal to psin, calculate < (x1 -...

Problem 5.5 In David Griffiths “Introduction to Quantum Mechanics” says: Imagine two non interacting particles, each of mass m, in the infinite square well. If one is in the state psin and the other in state psim orthogonal to psin, calculate < (x1 - x2) 2 >, assuming that (a) they are...

Hello everyone! Can anyone help me here in this theorems (prove)? (Or solve) 1. Suppose that A and B are square matrices and AB = 0. (as in zero matrix) If B is nonsingular, find A. 2. Show that if A is nonsingular symmetric matrix, then A^-1 is symmetric. I hope these won't...